For all the controversy he has generated over the years, Pecker has amazed even his most vociferous critics for his ability to walk a financial tightrope during the 10 turbulent years since he took over AMI, the owner of the National Enquirer, Star, Shape and Muscle & Fitness.

Starting in 2010, Pecker shepherded AMI through a pre-packaged bankruptcy that saw Thomas H. Lee Partners and Evercore lose their investments while bondholders had their debt converted to equity.

While Time Inc. hasn’t experienced that level of financial upheaval, its profits have declined from $1.3 billion seven years ago to just $420 million last year.

By comparison, Pecker has managed to keep AMI’s earnings steadily above $105 million for the past several years, despite intense pressure from the newsstand slump.

He’s usually managed that feat through drastic cuts. In his latest move, he fired the editorial staffs of Natural Health and Fit Pregnancy and is in the process of moving those magazines across the country to AMI’s New York offices in downtown Manhattan.

One Time Inc. insider predicted an exodus if Pecker got the job, as the Enquirer with its tradition of “checkbook journalism”— or paying sources for tips and stories — is seen as the polar opposite of the high-standard journalism practiced at Time Inc.

“It would really rock the journalists in the company,” the insider said.

On the other hand, a former Time Inc. insider said righting the ship will probably entail laying off most executives and hiring some back at 40 percent of their salaries.

“That’s what’s needed, but no CEO would want that kind of blood on his hands,” said the former editor.

Pecker, however, does not seem bothered by anger from the rank and file over some of his cost-cutting moves.

One insider with some knowledge of the search insisted that there was “zero chance” that the interview would result in a job offer.

Another name that surfaced but which appears to be a non-starter is Ross Levinsohn, the former interim chief executive of Yahoo! He recently became CEO of Guggenheim Digital Media, owner of The Hollywood Reporter, Billboard and Adweek, and is probably out of the running.

Insiders said Bewkes wants to wrap up the search before the summer.

Globe bids

First-round bids for the Boston Globe were due yesterday to Evercore, the investment bank handling the sale for the New York Times Co.

In 1993, the Times bought Affiliated Publications from the Taylor family, which had owned it for more than a century, for $1.1 billion. Affiliated was mostly the Globe, although it also included a collection of trade publications such as Adweek and Billboard.

Now the same family that reaped a bonanza from that sale may be interested in riding to the paper’s rescue with a plan to buy it back. Ben Taylor, a former publisher, and his first cousin, Steve Taylor, are said to be among the bidders.

The Wall Street Journal reported last week that the Taylor family is being advised by short-lived Time Inc. CEO Jack Griffin, who at one point was thinking of putting together his own investment group. Griffin is a Boston native whose father was once editor-in-chief of the Boston Herald.

In other bids, Heberden Ryan from Boston Post Partners is teaming up with Richard Daniels, another former Globe president, who was most recently running GateHouse Media New England.

Evercore is said to be seeking $100 million for the paper, along with the Worcester Telegraph & Gazette and other properties in the Times’ New England Media Group. But in today’s depressed newspaper market, there are some who think that is a stretch.

Other deep-pocketed bidders have not showed up in force.

Aaron Kushner — a greeting card entrepreneur who lived in Boston for a while and was interested the last time the paper was peddled in 2009 — has since gone on to buy the Orange County Register from Freedom Communications. He is said to be keeping his powder dry for a run at Tribune Co., which is expected to sell the Los Angeles Times, the Chicago Tribune and the rest of its newspaper portfolio later this year.

Blowing smoke

Former Mayor Rudy Giuliani took to the dais at the 21st annual Night to Remember — a fund-raiser for the Prostate Cancer Foundation hosted by Cigar Aficionado and Wine Spectator owner Marvin Shanken — and poked fun at Mike Bloomberg’s “nanny state.”

Before a cigar-puffing crowd that included Rush Limbaugh, Michael Milken and Conde Nast’s Jonathan Newhouse, Giuliani joked that Shanken plans to start a new magazine called “16 Ounce.”

He explained that under the recently proposed regulations to ban sugary sodas, patrons would have been allowed to bring empty 16-ounce glasses into an establishment and pour in the contents of two 8-ounce sodas. Giuliani said that opens up a market niche for the new publication.

“When I was mayor, we worried about things like murder, rape, poverty, unemployment, education,” said Giuliani. “It’s nice to know that I did such a good job that this is what they worry about now.”.